The present paper provides novel results on the model theory of Independence friendly modal logic. We concentrate on its particularly well-behaved fragment that was introduced in Tulenheimo and Sevenster (Advances in Modal Logic, 2006). Here we refer to this fragment as ‘Simple IF modal logic’ (IFML s ). A model-theoretic criterion is presented which serves to tell when a formula of IFML s is not equivalent to any formula of basic modal logic (ML). We generalize the notion of bisimulation familiar (...) from ML; the resulting asymmetric simulation concept is used to prove that IFML s is not closed under complementation. In fact we obtain a much stronger result: the only IFML s formulas admitting their classical negation to be expressed in IFML s itself are those whose truth-condition is in fact expressible in ML. (shrink)

We analyze the expressive resources of \ logic that do not stem from Henkin quantification. When one restricts attention to regular \ sentences, this amounts to the study of the fragment of \ logic which is individuated by the game-theoretical property of action recall. We prove that the fragment of prenex AR sentences can express all existential second-order properties. We then show that the same can be achieved in the non-prenex fragment of AR, by using “signalling by disjunction” instead of (...) Henkin or signalling patterns. We also study irregular IF logic and analyze its correspondence to regular IF logic. By using new methods, we prove that the game-theoretical property of knowledge memory is a first-order syntactical constraint also for irregular sentences, and we identify another new first-order fragment. Finally we discover that irregular prefixes behave quite differently in finite and infinite models. In particular, we show that, over infinite structures, every irregular prefix is equivalent to a regular one; and we present an irregular prefix which is second order on finite models but collapses to a first-order prefix on infinite models. (shrink)